Halftone imaging, sometimes referred to simply as “halftoning,” is a well-known technique for transforming a continuous tone or gray scale image (e.g., a photograph or a digital image) having picture elements or “pixels” that have tones whose values vary continuously or over a large number of discrete gray levels, into a halftone image having pixels that are either black (presence of a mark or “dot”) or white (absence of a mark or “dot”). Although the absence of a black dot can be considered a white dot, for ease of discussion, the term “dot”, as used herein, refers to the presence of a black dot. In general, the halftone image creates the illusion of continuous tone. In color printers, the illusion of continuous shades of color is produced by superimposing the halftones of the individual colorants used, e.g., cyan, magenta, yellow and black (CYMK).
Halftoning can be performed by modulating the size or amplitude of the dots, which is sometimes referred to as “amplitude modulation” or AM, or by modulating the spacing or frequency of the dots, which is sometimes referred to as “frequency modulation” or FM. A combination of AM and FM halftoning, sometimes referred to as “AM/FM halftoning,” simultaneously modulates dot size and dot density. With AM halftoning, the viewer of the printed halftone image will perceive areas of the halftone image having larger dots to have a darker gray level than areas of the halftone image having smaller dots. With FM halftoning, the viewer of the printed halftone image will perceive areas of the halftone image having a greater density of dots to have a darker gray level than areas of the halftone image having a lesser density of dots. With AM/FM halftoning, the viewer of the printed halftone image will perceive areas of the halftone image having a greater density of and/or larger dots to have a darker gray level than areas of the halftone image having a lesser density of and/or smaller dots.
Another halftoning technique is to transform a gray scale image to a halftone image using a dither matrix or halftone screen. The dither matrix consists of a two-dimensional array of elements, each having a value v ranging from 0 to (z−1), where z represents the total number of gray levels within the gray scale range being used. For example, when using a gray scale range of 0 through 255, where 0 represents white and 255 represents black, 0≦v≦255. The number of elements in the dither matrix can be smaller than or equal to the number of pixels in the gray scale image to be transformed. The dither matrix is mapped over the gray scale image. For a gray scale image that is larger than the dither matrix, the dither matrix is replicated or tiled to cover the entire gray scale image. Each pixel in the gray scale image is compared to a corresponding element in the halftone screen. If the gray scale image pixel has a larger or equal value, a dot is formed in the corresponding position of the halftone image, assuming an ascending gray level numbering convention is employed, i.e., where higher gray level numbers correspond to darker gray levels. Conversely, if a descending gray level numbering convention is employed, i.e., where higher gray level numbers correspond to lighter gray levels, then no dot is formed in the corresponding position of the halftone image if the gray scale image pixel has a larger value than the corresponding element of the halftone screen. When printing such a halftone image, the printing engine will print a dot for each position or location in the halftone image in which a dot has been formed.
It is desirable that the halftoning process produce a halftone image that is virtually indistinguishable from the gray scale image being reproduced. In order to achieve such a result, the gray level patterns in the halftone image should be as imperceptible as possible to the human eye. To this end, halftone screens have been designed to achieve a pseudo-random or stochastic distribution of dots over the halftone image. Such halftone screens are sometimes referred to as “stochastic screens.”
Some imaging devices are incapable of stably or reliably producing dots beyond a certain horizontal dot resolution. For example, some laser printers operate in an enhanced resolution imaging mode, sometimes referred to as a High Definition Imaging (HDI) mode, in which the laser horizontal scan line of the normal resolution mode is subdivided into finer increments, whereby the laser print engine must produce dots during correspondingly shorter laser on/off cycles. In other words, each pixel of the halftone image produced by the laser printer in the enhanced resolution mode is subdivided into sub-pixels. For example, if the normal horizontal resolution mode of a laser printer is 600 dots per inch (dpi), and the enhanced horizontal resolution mode of that laser printer is 2,400 dpi, then each pixel of the halftone image produced by that laser printer in the enhanced horizontal resolution mode is subdivided into 4 sub-pixels, so that the laser on/off cycle in the enhanced horizontal resolution mode is ¼th the laser on/off cycle in the normal horizontal resolution mode. However, the laser printer engine may be incapable of stably or reliably printing isolated “sub-pixel dots” at that sub-pixel resolution, which results in perceptible visual anomalies or quantization noise in the resultant half-tone image produced by the laser printer. Such instability of the image forming device is referred to herein as “dot instability”.
It is has been found desirable to force a certain level of dot clustering in a halftone image in order to minimize perceptible quantization noise in the halftone image attributable to dot instability of the image forming device. A halftone screen designed to produce a halftone image having a stochastic distribution and clustering of dots is sometimes referred to as a “clustered-dot stochastic halftone screen.” Clustered-dot stochastic screen designs can be used to design high quality clustered-dot stochastic screens that are moiré and pattern free, and that are also less likely to show bands, even when printing halftone images with a laser printer or other printers that have printing engines that exhibit dot-to-dot interactions. Further, clustered-dot stochastic halftone screens can be used to produce a halftone image that exhibits halftone noise which is very similar to the grain noise in a photograph, whereby the halftone image better resembles a real photograph. The filter parameters can be adjusted in order to produce a stochastic patterning of dot clusters in the output halftone image which vary in both their size and in their spacing. For example, it may be desirable to produce halftone images with large clusters in printers with high dot-gain characteristics and small clusters in printers with low dot-gain characteristics.
However, it is desirable to generate a halftone screen that achieves a desired statistical distribution of dots (“spatial characteristics”) in an output halftone image (e.g., with respect to average dot size and/or average inter-minority pixel distance), in a manner that minimizes the need for experimentation on the part of the screen designer in order to achieve this result. It would also be desirable to generate a color halftone screen having such attributes for color halftoning applications.